Best match graphs

Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let T be a phylogenetic (gene) tree T and σ an assignment of leaves of T to species. The best match graph (G,σ) is a digraph that contains an arc from x to y if the genes x and y reside in different species and y is one of possibly many (evolutionary) closest relatives of x compared to all other genes contained in the species σ(y). Here, we characterize best match graphs and show that it can be decided in cubic time and quadratic space whether (G,σ) derived from a tree in this manner. If the answer is affirmative, there is a unique least resolved tree that explains (G,σ), which can also be constructed in cubic time

A Unifying View on Recombination Spaces and Abstract Convex Evolutionary Search

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Proceedings of EvoCOP 2019 - 19th European Conference on Evolutionary Computation, 24-26 April 2019, Leipzig, GermanyPrevious work proposed to unify an algebraic theory of fitness landscapes and a geometric framework of evolutionary algorithms (EAs). One of the main goals behind this unification is to develop an analytical method that verifies if a problem's landscape belongs to certain abstract convex landscapes classes, where certain recombination-based EAs (without mutation) have polynomial runtime performance. This paper advances such unification by showing that: (a) crossovers can be formally classified according to geometric or algebraic axiomatic properties; and (b) the population behaviour induced by certain crossovers in recombination-based EAs can be formalised in the geometric and algebraic theories. These results make a significant contribution to the basis of an integrated geometric-algebraic framework with which analyse recombination spaces and recombination-based EAs

Monotonicity of Fitness Landscapes and Mutation Rate Control

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms

The Ascent of the Abundant: How Mutational Networks Constrain Evolution

Evolution by natural selection is fundamentally shaped by the fitness landscapes in which it occurs. Yet fitness landscapes are vast and complex, and thus we know relatively little about the long-range constraints they impose on evolutionary dynamics. Here, we exhaustively survey the structural landscapes of RNA molecules of lengths 12 to 18 nucleotides, and develop a network model to describe the relationship between sequence and structure. We find that phenotype abundance—the number of genotypes producing a particular phenotype—varies in a predictable manner and critically influences evolutionary dynamics. A study of naturally occurring functional RNA molecules using a new structural statistic suggests that these molecules are biased toward abundant phenotypes. This supports an “ascent of the abundant” hypothesis, in which evolution yields abundant phenotypes even when they are not the most fit

On the relationship between the macroevolutionary trajectories of morphological integration and morphological disparity

How does the organization of phenotypes relate to their propensity to vary? How do evolutionary changes in this organization affect large-scale phenotypic evolution? Over the last decade, studies of morphological integration and modularity have renewed our understanding of the organizational and variational properties of complex phenotypes. Much effort has been made to unravel the connections among the genetic, developmental, and functional contexts leading to differential integration among morphological traits and individuation of variational modules. Yet, their macroevolutionary consequences on the dynamics of morphological disparity-the large-scale variety of organismal designs-are still largely unknown. Here, I investigate the relationship between morphological integration and morphological disparity throughout the entire evolutionary history of crinoids (echinoderms). Quantitative analyses of interspecific patterns of variation and covariation among characters describing the stem, cup, arm, and tegmen of the crinoid body do not show any significant concordance between the temporal trajectories of disparity and overall integration. Nevertheless, the results reveal marked differences in the patterns of integration for Palaeozoic and post-Palaeozoic crinoids. Post-Palaeozoic crinoids have a higher degree of integration and occupy a different region of the space of integration patterns, corresponding to more heterogeneously structured matrices of correlation among traits. Particularly, increased covariation is observed between subsets of characters from the dorsal cup and from the arms. These analyses show that morphological disparity is not dependent on the overall degree of evolutionary integration but rather on the way integration is distributed among traits. Hence, temporal changes in disparity dynamics are likely constrained by reorganizations of the modularity of the crinoid morphology and not by changes in the variability of individual traits. The differences in integration patterns explain the more stereotyped morphologies of post-Palaeozoic crinoids and, from a broader macroevolutionary perspective, call for a greater attention to the distributional heterogeneities of constraints in morphospace

The topology of evolutionary biology

Central notions in evolutionary biology are intrinsically topological. This claim is maybe most obvious for the discontinuities associated with punctuated equilibria. Recently, a mathematical framework has been developed that derives the concepts of phenotypic characters and homology from the topological structure of the phenotype space. This structure in turn is determined by the genetic operators and their interplay with the properties of the genotype-phenotype map